The utilisation of hydrogen in ships has important potential in terms of achieving the decarbonisation of waterway transport, which produces approximately 3% of the world’s total emissions. However, the utilisation of hydrogen drives in maritime and inland shipping is conditioned by the efficient and safe storage of hydrogen as an energy carrier on ship decks. Regardless of the type, the constructional design and the purpose of the aforesaid vessels, the preferred method for hydrogen storage on ships is currently high-pressure storage, with an operating pressure of the fuel storage tanks amounting to tens of MPa. Alternative methods for hydrogen storage include storing the hydrogen in its liquid form, or in hydrides as adsorbed hydrogen and reformed fuels. In the present article, a method for hydrogen storage in metal hydrides is discussed, particularly in a certified low-pressure metal hydride storage tank—the MNTZV-159. The article also analyses the 2D heat conduction in a transversal cross-section of the MNTZV-159 storage tank, for the purpose of creating a final design of the shape of a heat exchanger (intensifier) that will help to shorten the total time of hydrogen absorption into the alloy, i.e., the filling process. Based on the performed 3D calculations for heat conduction, the optimisation and implementation of the intensifier into the internal volume of a metal hydride alloy will increase the performance efficiency of the shell heat exchanger of the MNTZV-159 storage tank. The optimised design increased the cooling power by 46.1%, which shortened the refuelling time by 41% to 2351 s. During that time, the cooling system, which comprised the newly designed internal heat transfer intensifier, was capable of eliminating the total heat from the surface of the storage tank, thus preventing a pressure increase above the allowable value of 30 bar.